1. **State the problem:** We have a rectangular section with base length $3x$ and area $6x^2 + 9x$. We want to find the height of the rectangle. 2. **Formula used:** The area $A$ of a rectangle is given by the formula: $$A = \text{base} \times \text{height}$$ 3. **Apply the formula:** Given the base $3x$ and area $6x^2 + 9x$, we set up the equation: $$6x^2 + 9x = 3x \times \text{height}$$ 4. **Solve for height:** Divide both sides by $3x$ (assuming $x \neq 0$): $$\text{height} = \frac{6x^2 + 9x}{3x}$$ 5. **Simplify the expression:** Factor numerator: $$6x^2 + 9x = 3x(2x + 3)$$ Substitute back: $$\text{height} = \frac{3x(2x + 3)}{3x}$$ Cancel $3x$: $$\text{height} = 2x + 3$$ 6. **Interpretation:** The height of the rectangle is $2x + 3$. **Final answer:** $$\boxed{2x + 3}$$